{"paper":{"title":"$(H_p-L_p)$ type inequalities for subsequences of N\\\"orlund means of Walsh-Fourier series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David Baramidze, George Tephnadze, Kristoffer Tangrand, Lars-Erik Persson","submitted_at":"2023-03-03T11:00:17Z","abstract_excerpt":"We investigate the subsequence $\\{t_{2^n}f \\}$ of N\\\"{o}rlund means with respect to the Walsh system generated by non-increasing and convex sequences. In particular, we prove that a big class of such summability methods are not bounded from the martingale Hardy spaces $H_p$ to the space $weak-L_p $ for $0<p<1/(1+\\alpha) $, where $0<\\alpha<1$. Moreover, some new related inequalities are derived. As application, some well-known and new results are pointed out for well-known summability methods, especially for N\\\"{o}rlund logarithmic means and Ces\\`aro means."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01846","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.01846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}